Problem: $ F = \left[\begin{array}{rrr}3 & 4 & 7 \\ 5 & 6 & 2\end{array}\right]$ What is $ F^{T}$ ?
To find the transpose, swap the rows and columns. $ F^{T}$ = $\left[\begin{array}{rr}3 & 5 \\ 4 & 6 \\ 7 & 2\end{array}\right]$